Invariants
Level: | $168$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}19&60\\26&157\end{bmatrix}$, $\begin{bmatrix}41&24\\70&127\end{bmatrix}$, $\begin{bmatrix}49&156\\162&61\end{bmatrix}$, $\begin{bmatrix}71&12\\92&139\end{bmatrix}$, $\begin{bmatrix}139&102\\166&161\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.ls.3 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
Cyclic 168-torsion field degree: | $768$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-12.a.2.10 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.o.2.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.o.2.13 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-168.di.1.16 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.di.1.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
168.384.5-168.je.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ji.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.jo.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ju.3.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.jv.4.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ka.3.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kq.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kv.4.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.os.4.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ot.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.pd.2.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.pe.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.pj.2.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.pl.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.qe.2.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.qg.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |